$(5$ points$)$ The displacement of a transverse wave on a string is given by the equation

$y(x,t)=$Acos$[\frac{2}{}(x-vt)]$

If the amplitude of a wave is $0\mathrm{.}100cm,$ wavelength of $10\mathrm{.}0cm$ and speed $v$ of $5\mathrm{.}00c\frac{m}{s}.$

$($a$)(2$ points$)$ Calculate $y(x,t)$ at $t=0$ and $x=0,1\mathrm{.}5cm,3\mathrm{.}0cm,$cdots,$10\mathrm{.}0cm($as in for $7$ points from $x=0\mathrm{.}0cm$ to $10\mathrm{.}0cm$ at $1\mathrm{.}5cm$ intervals, you may use Excel or Python to help$).$ Plot the results to get the shape of the string at time $t=0.$

$($b$)(1$ point$)$ Repeat the above for $y(x,t)$ at $t=0\mathrm{.}100s.$

$($c$)(1$ point$)$ Repeat the above for $y(x,t)$ at $t=0\mathrm{.}200s.$

$($d$)(1$ point$)$ What direction is the wave travelling in based on the results above?